My understanding of frozen pipes is that 20 degrees F is the rule of thumb.
Its good that you already drained as much as you can but there will be a problem with anything left in traps and low points.
As a precaution, you might want to call the owner of the storage yard and ask them to open all faucets. This should provide relief from the excessive pressure that builds between the faucet and the ice blockage if and when freezing occurs. Basically, if there is no excessive water pressure, there should be no burst pipe, even if the water inside the pipe were to freeze. Opening the faucets is not a replacement for proper winterizing, but it seems logical to me that it should help until you get there to winterize.
Engineers - Feel free to correct if anything is wrong with this.
DW, 3 Kids and our Goldens
2012 Shamrock 233S
2008 Toyota Sequoia 5.7L 4WD